ABSTRACTIn 1993, Museums Australia, representing museums and the Australian museum community, adopted a policy covering relations between museums and Australia's indigenous peoples.Previous Possessions, New Obligationsis based on 13 principles, the first of which recognizes the right to self‐determination of Aboriginal and Torres Strait Islander peoples in respect of their cultural property. The policy recognizes a multiplicity of interests in indigenous peoples' cultural property but emphasizes Aboriginal and Torres Strait Islander peoples' primary role.The policy was developed through consultation with indigenous people and communities, museums, professional associations, and governments. It covers human remains, secret/sacred material, and collections in general. It also deals with museums' public programs and issues of staffing, training, and governance. It emphasizes the importance of consultation between museum staff and appropriate persons and communities when museums are dealing with indigenous cultures.This paper traces the history of museums' dealings with indigenous peoples in several countries, especially Australia. The development of this policy from mid‐1991 is traced.Museums Australia, in collaboration with the Australian government, is pursuing the policy, especially the provenancing of human remains and secret/sacred material, to assist in returning such material when requested and appropriate. Museums Australia is also reviewing the effect the policy has had over the last two years. While the policy is an important document, there is still much progress to be m